\(\mathcal{L}^p\)-approximation using fractal functions on the Sierpiński gasket
After recalling the definition of iterated function system (IFS) as originally introduced by Barnsley \& Demko, the authors review fractal interpolation on the Sierpiński gasket (SG) and investigate the approximation of functions by fractal functions defined on SG in the \(\mathcal{L}^p\)-norm. Properties of the associated fractal operator \(\mathcal{F}^\alpha\) are also presented in this context. Lastly, dimension-preserving approximation in the \(\mathcal{L}^p\)-norm is discussed.
scientific article; zbMATH DE number 7490185
scientific article